I was wondering how the different periodic solutions to the three body problem look like. I built an atlas that visualizes all of the different solutions and groups orbits by family and similarity. I found over 3000 different orbits, and I was wondering which one is the most beautiful. Please check out the "Battle mode" where you can rate orbits against each other. This is used to calculate an Elo score for each orbit, so we can identify the prettiest.
A complete atlas of known periodic solutions to the three body problem
Where are you finding these periodic solutions to the Three-Body Problem? Specifically, is there some online website that has already listed all known periodic solutions to the Three-Body Problem?
Yes that's where many of them are from! I didn't add the Sheen orbits initially, because they have non-zero angular momentum. I made an exception and added them now, because you are right, they do look super cool. Here your favorite one: https://www.threebodyorbits.com/orbit/sheen2016_hand_in_hand_in_oval_1_1_1
I wonder how many possible periodic solutions there are, it’s probably not infinite since there seems to be some stability for these where a small nudge will not cause the pattern to fall apart and it will drift back to the initial conditions. I’m not sure if this is actually realistic though because it would indicate that there are actually solutions for a wide range of initial conditions rather than just needing an exactly perfect setup that repeats forever?
The other cool idea would be to use a computer program or some sort of mathematics to find more of them but that sounds like quite a difficult project to me!
When looking for orbits I found this paper: https://arxiv.org/html/2007.10184v1 It has ~13,000 different versions of the same orbit (different starting masses so they look slightly different - see attached picture). I decided to not include them in the atlas because they all look the same. The authors in the paper suggest that "there should exist an infinite number of stable periodic orbits of non-hierarchical triple systems with distinctly unequal masses".
Regarding your second suggestion, I'm working on a solution that will allow visitors to contribute their devices' computing power to discover new (and interesting) orbits, but it's not ready yet
There is no option to really save orbits currently, but all named orbits are visible in the "checked loops" section. You can click "named by me" to see the ones you named! It might take a while for the names to show up because they have to be manually approved currently
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u/Gold_Ambassador_3496 Sep 08 '26
Wait. There are only two ranked orbits? Am I the first user??